A316518 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 28, 49, 16, 32, 120, 75, 75, 120, 32, 64, 293, 174, 204, 174, 293, 64, 128, 719, 414, 619, 619, 414, 719, 128, 256, 1774, 1002, 1710, 2995, 1710, 1002, 1774, 256, 512, 4389, 2398, 4894, 11977, 11977, 4894, 2398, 4389, 512, 1024

Offset

1,2

Comments

Table starts

...1....2....4.....8.....16.......32........64........128..........256

...2....8...21....49....120......293.......719.......1774.........4389

...4...21...28....75....174......414......1002.......2398.........5743

...8...49...75...204....619.....1710......4894......14053........40063

..16..120..174...619...2995....11977.....48677.....201771.......826524

..32..293..414..1710..11977....73031....432088....2685906.....16394959

..64..719.1002..4894..48677...432088...3646656...32938897....290133839

.128.1774.2398.14053.201771..2685906..32938897..442204876...5767984330

.256.4389.5743.40063.826524.16394959.290133839.5767984330.110715247064

Links

R. H. Hardin, Table of n, a(n) for n = 1..311

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5

k=3: a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +a(n-4) -a(n-5) for n>8

k=4: [order 10] for n>13

k=5: [order 25] for n>28

k=6: [order 44] for n>49

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..1..1..1. .0..0..0..0. .0..0..0..0
..0..1..1..1. .1..1..1..0. .0..1..1..1. .0..0..0..0. .0..0..1..0
..1..1..1..1. .1..1..1..1. .1..0..1..1. .0..0..0..0. .0..0..1..0
..1..1..0..1. .1..1..1..1. .1..1..1..1. .0..1..0..0. .0..0..0..0
..0..0..1..1. .1..1..1..1. .0..1..1..0. .1..0..0..1. .0..0..0..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303721.

Sequence in context: A303727 A305230 A304775 * A304472 A316289 A306053

Adjacent sequences: A316515 A316516 A316517 * A316519 A316520 A316521

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 05 2018

Status

approved